Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  cgsexg Unicode version

Theorem cgsexg 3142
 Description: Implicit substitution inference for general classes. (Contributed by NM, 26-Aug-2007.)
Hypotheses
Ref Expression
cgsexg.1
cgsexg.2
Assertion
Ref Expression
cgsexg
Distinct variable groups:   ,   ,

Proof of Theorem cgsexg
StepHypRef Expression
1 cgsexg.2 . . . 4
21biimpa 484 . . 3
32exlimiv 1722 . 2
4 elisset 3120 . . . 4
5 cgsexg.1 . . . . 5
65eximi 1656 . . . 4
74, 6syl 16 . . 3
81biimprcd 225 . . . . 5
98ancld 553 . . . 4
109eximdv 1710 . . 3
117, 10syl5com 30 . 2
123, 11impbid2 204 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-12 1854  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111
 Copyright terms: Public domain W3C validator